Precalculus Examples
x2-(3-y)2=24x2−(3−y)2=24
Step 1
Step 1.1
Simplify each term.
Step 1.1.1
Rewrite (3-y)2(3−y)2 as (3-y)(3-y)(3−y)(3−y).
x2-((3-y)(3-y))=24x2−((3−y)(3−y))=24
Step 1.1.2
Expand (3-y)(3-y)(3−y)(3−y) using the FOIL Method.
Step 1.1.2.1
Apply the distributive property.
x2-(3(3-y)-y(3-y))=24x2−(3(3−y)−y(3−y))=24
Step 1.1.2.2
Apply the distributive property.
x2-(3⋅3+3(-y)-y(3-y))=24x2−(3⋅3+3(−y)−y(3−y))=24
Step 1.1.2.3
Apply the distributive property.
x2-(3⋅3+3(-y)-y⋅3-y(-y))=24x2−(3⋅3+3(−y)−y⋅3−y(−y))=24
x2-(3⋅3+3(-y)-y⋅3-y(-y))=24x2−(3⋅3+3(−y)−y⋅3−y(−y))=24
Step 1.1.3
Simplify and combine like terms.
Step 1.1.3.1
Simplify each term.
Step 1.1.3.1.1
Multiply 33 by 33.
x2-(9+3(-y)-y⋅3-y(-y))=24x2−(9+3(−y)−y⋅3−y(−y))=24
Step 1.1.3.1.2
Multiply -1−1 by 33.
x2-(9-3y-y⋅3-y(-y))=24x2−(9−3y−y⋅3−y(−y))=24
Step 1.1.3.1.3
Multiply 33 by -1−1.
x2-(9-3y-3y-y(-y))=24x2−(9−3y−3y−y(−y))=24
Step 1.1.3.1.4
Rewrite using the commutative property of multiplication.
x2-(9-3y-3y-1⋅(-1y⋅y))=24x2−(9−3y−3y−1⋅(−1y⋅y))=24
Step 1.1.3.1.5
Multiply yy by yy by adding the exponents.
Step 1.1.3.1.5.1
Move yy.
x2-(9-3y-3y-1⋅(-1(y⋅y)))=24x2−(9−3y−3y−1⋅(−1(y⋅y)))=24
Step 1.1.3.1.5.2
Multiply yy by yy.
x2-(9-3y-3y-1⋅(-1y2))=24x2−(9−3y−3y−1⋅(−1y2))=24
x2-(9-3y-3y-1⋅(-1y2))=24x2−(9−3y−3y−1⋅(−1y2))=24
Step 1.1.3.1.6
Multiply -1−1 by -1−1.
x2-(9-3y-3y+1y2)=24x2−(9−3y−3y+1y2)=24
Step 1.1.3.1.7
Multiply y2y2 by 11.
x2-(9-3y-3y+y2)=24x2−(9−3y−3y+y2)=24
x2-(9-3y-3y+y2)=24x2−(9−3y−3y+y2)=24
Step 1.1.3.2
Subtract 3y3y from -3y−3y.
x2-(9-6y+y2)=24x2−(9−6y+y2)=24
x2-(9-6y+y2)=24x2−(9−6y+y2)=24
Step 1.1.4
Apply the distributive property.
x2-1⋅9-(-6y)-y2=24x2−1⋅9−(−6y)−y2=24
Step 1.1.5
Simplify.
Step 1.1.5.1
Multiply -1−1 by 99.
x2-9-(-6y)-y2=24x2−9−(−6y)−y2=24
Step 1.1.5.2
Multiply -6−6 by -1−1.
x2-9+6y-y2=24x2−9+6y−y2=24
x2-9+6y-y2=24x2−9+6y−y2=24
x2-9+6y-y2=24x2−9+6y−y2=24
Step 1.2
Reorder.
Step 1.2.1
Move -9−9.
x2+6y-y2-9=24x2+6y−y2−9=24
Step 1.2.2
Move 6y6y.
x2-y2+6y-9=24x2−y2+6y−9=24
x2-y2+6y-9=24x2−y2+6y−9=24
x2-y2+6y-9=24x2−y2+6y−9=24
Step 2
Step 2.1
Subtract 2424 from both sides of the equation.
x2-y2+6y-9-24=0x2−y2+6y−9−24=0
Step 2.2
Subtract 2424 from -9−9.
x2-y2+6y-33=0x2−y2+6y−33=0
x2-y2+6y-33=0x2−y2+6y−33=0